Squeeze flow of a viscoplastic Bingham medium: an asymptotic solution

TL;DR

This paper develops an asymptotic solution for the squeeze flow of a viscoplastic Bingham medium, revealing that the plug region is a pseudo-plug that is weakly yielded, refining previous lubrication-based models.

Contribution

It introduces an asymptotic approach that accurately characterizes the pseudo-plug region in viscoplastic squeeze flow, improving upon standard lubrication approximations.

Findings

The plug region is actually weakly yielded at higher order.

Standard lubrication models overestimate the plug's rigidity.

The solution provides a more accurate description of the flow dynamics.

Abstract

We obtain an asymptotic solution for the squeeze flow of a viscoplastic medium. The standard lubrication-style expansions of the problem predict plug speed which varies slowly in the principal flow direction. This variation implies that the plug region cannot be truly unyielded. Our solution shows that this region is a pseudo-plug region in which the leading order equation predict a plug, but really it is weakly yielded at higher order.